(1) 设 $f, g$ 为连续可微函数, $u=f(x, x y), v=g(x+x y)$, 求 $\frac{\partial u}{\partial x} \cdot \frac{\partial v}{\partial x}$.
(2) 设矩阵 ${A}$ 和 ${B}$ 满足关系式 ${A B}={A}+2 {B}$, 其中 ${A}=\left(\begin{array}{lll}3 & 0 & 1 \\ 1 & 1 & 0 \\ 0 & 1 & 4\end{array}\right)$, 求矩阵 ${B}$.
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